Spatial SIR dynamics obey a Fisher-KPP-type PDE: ∂I/∂t = D·∂²I/∂x² + rI(S-I) - γI. The reaction term combines logistic growth and recovery. A traveling wave solution I(x,t) = f(x - ct) exists with minimum speed c* = 2√(Dr) (pulled wave: the front is driven by the low-density tip). Initial conditions with compact support → wave selects c*. Steeper initial profiles → pushed waves with c>c*. The S (susceptible) population is depleted behind the wave front, creating a spatial epidemic chain.